International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 35, Pages 1855-1879

Maximum principle and its extension for bounded control problems with boundary conditions

Olga Vasilieva

Department of Mathematics, University of Valle, Cali, Colombia

Received 5 August 2003

Copyright © 2004 Olga Vasilieva. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This note is focused on a bounded control problem with boundary conditions. The control domain need not be convex. First-order necessary condition for optimality is obtained in the customary form of the maximum principle, and second-order necessary condition for optimality of singular controls is derived on the basis of second-order increment formula using the method of increments along with linearization approach.